Temporal Constraints on Trajectories in Qualitative Simulation

Giorgio Brajnik and Daniel J. Clancy

We present a new method for specifying temporal constraints on trajectories of dynamical systems enforcing them during qualitative simulation. Such constraints are otherwise inexpressible using standard qualitative reasoning techniques. Trajectory constraints can be used to restrict the simulation to a region of the state space and to inject discontinuities. This capability can be used to focus the simulation for larger, more complex simulations, simulate nonautonomous and piecewise-continuous systems, reason about boundary condition problems and incorporate observations into the simulation. The method been implemented in TeQSIM, a qualitative simulator. It combines the expressive power of qualitative differential equations with temporal logic by interleaving temporal logic model checking with the simulation constrain and refine the resulting predicted behaviors and to inject discontinuous changes into the simulation. The paper discusses the applicability of temporal constraints in tasks ranging from simulation to monitoring and control of continuous dynamical systems. present a real-world control problem in the domain water supply. Finally, the basic algorithm and theoretical results (soundness and completeness) are described.

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